There is a modern-day ghost story at the heart of the British political system. Admittedly there are probably several, but this one is of the more stunning variety. Lord Roskill, when confronted with its murky depths in 1985, could hear: "the clanking of medieval chains of the ghosts of the past ... the anarchism of past centuries."

What is it? Here are some clues. It's a bit like a private members' club. To join it, you have to take an oath that you will "to your uttermost bear Faith and Allegiance to the Queen's Majesty; and assist and defend ... against all Foreign Princes".

Your membership will be for life and you will "enjoy precedence following Knights of the Garter and of the Thistle, next after the eldest sons of barons". Your background is likely to be a close relative of the Queen, a "noblemen of high rank", a "person eminent in science or letters", an archbishop or maybe just someone owed a favour by the government of the day. And best of all, you will get to pass laws without being inconvenienced by the interference of a democratically elected parliament, for example.

Welcome to the privy council – a body so obscure that it makes the House of Lords seem positively modern. The Lords may get to amend laws, financial inducements notwithstanding – this lot get to actually pass them, and no one even knows who they are. Even the recent meticulous attempt to lay bare what the privy council actually does, in a recently released report by QC Patrick O'Connor, left some of the mystery intact. It's difficult to explain what the privy council does because it's not exactly written down anywhere. It has more or less "evolved" (although that seems like a generous concept to apply in this context) since the Norman and Plantagenet kings of the 12th century.

In those days, the monarch exercised real political power, and needed a council of advisors to help him decide how to use it. And who better to provide that advice in medieval England than a council of bishops, peers and knights?

The thing is, in 2009, a glorious revolution later, not to mention the general acceptance of such concepts of universal suffrage, democratic elections and accountable government, the privy council is still full of bishops, peers and knights.

These days, mainly as a result of those developments, the idea of the Queen exercising any of her prerogative powers (constitutionally she still has an impressive range of them) personally, is unthinkable. It wouldn't be illogical to assume that as a result, the privy council would be rendered redundant.

Instead, it is far from redundant. It has essentially become a mechanism for the government, which exercises the Queen's legal powers on her behalf, to make decisions away from public scrutiny.

Many of these powers are random and unlikely to be fought over by any other part of the state. Proclaiming the dates of bank holidays, deciding on the closure of burial grounds, appointing a new chairman of the BBC – well, maybe not so much the last one.

But others, known as prerogative "orders in council" give the privy council the power to make laws. These laws, which have the same status as primary legislation, are often the kind that would probably have a hard time if parliament – who we elected, by the way – were ever able to get their hands on them.

Evicting inhabitants from an island off the coast of Mauritius in return for some missile deal with the US. Banning union membership among civil servants. Freezing the bank accounts and controlling the expenditure of British citizens and their families without any judicial oversight. These are not the kind of issues that would go unnoticed in the Commons. Even the judicial committee of the House of Lords felt "judicial distress and indignation" when confronted with the sheer unaccountable audacity of this power.

This is not to say the privy council is without its charm. It's hard not to be amused at the idea of newly initiated cabinet members spending over an hour at Buckingham Palace rehearsing how to stand, kneel, raise right hands and retreat, or marvel at the obscurity of the annual ceremony of "pricking the sheriffs" with a bodkin – I have no idea what this means but it is one of the reasons that O'Connor's report makes such good reading.

But ceremony aside, it's hard to imagine there is anything about the privy council's law-making powers remotely consistent with modern democracy. Labour, before they came into power, appear to have agreed. Maybe when they realised how convenient it is to make laws without the hassle of parliament getting involved, they changed their minds. It's hard to imagine now however, that an organ of state so opaque that the House of Lords is utterly transparent by comparison, can really survive intact.